M. Esole

The $E_6$ Restricted Hyperplane Arrangement and its $E_7$ Shadow: Weyl Transport on a Minuscule Bruhat Poset

We study the restricted fan cut inside the dual fundamental Weyl chamber by the weights of a $27$-dimensional minuscule representation of $E_6$; the two such representations are dual and give the same arrangement. Only $11$ of the $27$ weights have kernels meeting its interior, and we prove that they determine the enti...